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Verifying a file system implementation
 In Sixth International Conference on Formal Engineering Methods (ICFEM’04), volume 3308 of LNCS
, 2004
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Simplifying proofs in Fitchstyle natural deduction systems
, 2004
"... We present an algorithm for simplifying Fitchstyle natural deduction proofs in classical firstorder logic. We formalize Fitchstyle natural deduction as a denotational proof language, N DL, with a rigorous syntax and semantics. Based on that formalization, we define an array of simplifying transfo ..."
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We present an algorithm for simplifying Fitchstyle natural deduction proofs in classical firstorder logic. We formalize Fitchstyle natural deduction as a denotational proof language, N DL, with a rigorous syntax and semantics. Based on that formalization, we define an array of simplifying transformations and show them to be terminating and to respect the formal semantics of the language. We also show that the transformations never increase the size or complexity of a deduction—in the worst case, they produce deductions of the same size and complexity as the original. We present several examples of proofs containing various types of superfluous “detours, ” and explain how our procedure eliminates them, resulting in smaller and cleaner deductions. All of the transformations are fully implemented in SMLNJ, and the complete code listing is available. 1.1
MachineCheckable Correctness Proofs for Intraprocedural Dataflow Analyses
"... This paper describes our experience using the interactive theorem prover Athena for proving the correctness of abstract interpretationbased dataflow analyses. For each analysis, our methodology requires the analysis designer to formally specify the property lattice, the transfer functions, and the ..."
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This paper describes our experience using the interactive theorem prover Athena for proving the correctness of abstract interpretationbased dataflow analyses. For each analysis, our methodology requires the analysis designer to formally specify the property lattice, the transfer functions, and the desired modeling relation between the concrete program states and the results computed by the analysis. The goal of the correctness proof is to prove that the desired modeling relation holds. The proof allows the analysis clients to rely on the modeling relation for their own correctness. To reduce the complexity of the proofs, we separate the proof of each dataflow analysis into two parts: a generic part, proven once, independent of any specific analysis; and several analysisspecific conditions proven in Athena.
Abductive Reasoning with Filtered Circumscription ∗
"... For logical artificial intelligence to be truly useful, its methods must scale to problems of realistic size. An interruptible algorithm enables a logical agent to act in a timely manner to the best of its knowledge, given its reasoning so far. This seems necessary to avoid analysis paralysis, tryin ..."
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For logical artificial intelligence to be truly useful, its methods must scale to problems of realistic size. An interruptible algorithm enables a logical agent to act in a timely manner to the best of its knowledge, given its reasoning so far. This seems necessary to avoid analysis paralysis, trying to think of every potentiality, however unlikely, beforehand. These considerations prompt us to look for alternative reasoning mechanisms for filtered circumscription, a nonmonotonic reasoning formalism used e.g. by Temporal Action Logic and Event Calculus. We generalize Ginsberg’s circumscriptive theorem prover and describe an interruptible theorem prover based on abduction that has been used to unify planning and reasoning in a logical agent architecture. 1
The Open University
"... Both empirical software engineering and humancomputer interaction (HCI) are applied sciences: studies conducted within these disciplines are futile unless they enhance, either directly or indirectly, the practice of software engineering in the former case, and computer support for human endeavours ..."
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Both empirical software engineering and humancomputer interaction (HCI) are applied sciences: studies conducted within these disciplines are futile unless they enhance, either directly or indirectly, the practice of software engineering in the former case, and computer support for human endeavours in the latter. The main thesis of this paper is that there should be improved communication between the two disciplines. We argue that a major current concern of researchers in empirical software engineering – that empirical studies do not sufficiently inform practice – and the current emphasis on studies following a traditional scientific experimental design, is very similar to the major concern and methodological emphasis of HCI in the late 1980s/early 1990s. HCI researchers responded to this concern by borrowing tools and techniques from other disciplines, as is currently being advocated by some in the world of empirical software engineering. Although this response has not been unequivocally successful in its aim of closing the gap between studies and practice, we believe that researchers in empirical software engineering might benefit from reflecting on the HCI experience.
A LOGIC FOR ‘BECAUSE’
"... Abstract. In spite of its significance for everyday and philosophical discourse, the explanatory connective ‘because ’ has not received much treatment in the philosophy of logic. The present paper develops a logic for ‘because ’ based on systematic connections between ‘because ’ and the truthfunctio ..."
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Abstract. In spite of its significance for everyday and philosophical discourse, the explanatory connective ‘because ’ has not received much treatment in the philosophy of logic. The present paper develops a logic for ‘because ’ based on systematic connections between ‘because ’ and the truthfunctional connectives. §1. Introduction. 1.1. The project. In the philosophy of logic, the natural language connectives ‘and’, ‘or’, ‘not’, and ‘if... then ’ are widely discussed and so are their formal counterparts, such as the truthfunctional connectives of classical logic or counterfactual and strict conditionals in modal systems. Considerably less attention has been paid to the explanatory
Contentbased encoding of mathematical and code libraries
"... This is a proposal for contentbased canonical naming of mathematical objects aimed at semantic machine processing, and an initial investigation of how useful it can be, how similar it is to other approaches, what disadvantages and limitations it has, and how it could be extended. 1 ..."
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This is a proposal for contentbased canonical naming of mathematical objects aimed at semantic machine processing, and an initial investigation of how useful it can be, how similar it is to other approaches, what disadvantages and limitations it has, and how it could be extended. 1
A Categorical Approach to Logics and Logic Homomorphisms
, 2007
"... This master’s thesis presents a number of important concepts in logic such as models, entailment, and proof calculi within the framework of category theory. By describing these concepts as categories, a tremendous amount of generality and power is gained. In particular, this approach makes it possib ..."
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This master’s thesis presents a number of important concepts in logic such as models, entailment, and proof calculi within the framework of category theory. By describing these concepts as categories, a tremendous amount of generality and power is gained. In particular, this approach makes it possible to reason about maps from one logic to another in a consistent and convenient manner. By a consistent map is meant that the truth stays invariant, that is, a statement true in the source logic is mapped to a similarly true statement in the target logic. Conversely, a statement false in the source logic is mapped to a statement false in the target logic. While the thesis focuses on the theoretical notions outlined above, a brief coverage of two practical applications is given as a means to illustrate the utility of these notions. Concluding the text is a chapter containing a discussion and a section wherein possible future work is presented. In an effort to make the text mostly selfcontained, concepts beyond basic discrete mathematics are duly introduced with definitions and examples. These include, for